President Barack Obama and the Centers for Disease Control and Prevention need to move more quickly to tighten restrictions on travelers coming to the U.S. from Ebola-afflicted areas, said Rep. Tim Murphy, R-Pa.

Murphy, a member of the GOP Doctors Caucus, told CNN Tuesday morning that the enhanced screening processes proposed so far by the CDC do not go far enough. Murphy wants to see some travel from West Africa restricted until visitors are proven virus-free.

The CDC has pushed back against tighter travel restrictions on Liberia, the African nation at the center of the epidemic, arguing that such rules could hamper the American-led effort to contain the outbreak.

"For [the CDC] to simply be dismissive and say 'We can't isolate those countries,' they're going down the wrong rabbit hole and trying to give the American public a false sense of security," Murphy said.

"The chance of getting this, spreading across 300 million Americans, is certainly very small. But the American public certainly is also saying 'We don't want this to be spreading at all,'" the congressman said.

"No one is saying, 'quarantine an entire continent.' What we're saying is more sophisticated screening, look at travel restrictions for individuals, continue to send aid there," the six-term congressman said. "We're not saying isolate everything from that. But right now the CDC is saying, 'It's OK for people to come and go, we'll just ask some questions.' It's not enough. I don't think the American public is comfortable with that. I hope in the next few days the CDC is going to ramp up other ways of screening folks and having more restrictions on people coming out of Africa."

Schumer on Sunday said screenings should include, “fever checks and health surveys in both airports and ports.” Murphy is chairman of the House Energy and Commerce Subcommittee on Oversight and Investigations, is scheduled to hold an Ebola hearing on Capitol Hill next week. The House Homeland Security Committee will hold its own Ebola hearing on Friday at the Dallas/Fort Worth International Airport.

That committee's chairman, Texas Republican Michael McCaul, said the hearing is being held at the airport to symbolize the interconnectedness of a world in which "threats to the homeland are only a flight away."

Correction, 3:40 p.m.: An earlier version of this article incorrectly stated the name of the committee and the time of the hearing. The hearing was last month before the House Foreign Affairs Committee.